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Simplifying -4.9x2 + 8.8x + 2.4 = 0 Reorder the terms: 2.4 + 8.8x + -4.9x2 = 0 Solving 2.4 + 8.8x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.4897959184 + -1.795918367x + x2 = 0 Move the constant term to the right: Add '0.4897959184' to each side of the equation. -0.4897959184 + -1.795918367x + 0.4897959184 + x2 = 0 + 0.4897959184 Reorder the terms: -0.4897959184 + 0.4897959184 + -1.795918367x + x2 = 0 + 0.4897959184 Combine like terms: -0.4897959184 + 0.4897959184 = 0.0000000000 0.0000000000 + -1.795918367x + x2 = 0 + 0.4897959184 -1.795918367x + x2 = 0 + 0.4897959184 Combine like terms: 0 + 0.4897959184 = 0.4897959184 -1.795918367x + x2 = 0.4897959184 The x term is -1.795918367x. Take half its coefficient (-0.8979591835). Square it (0.8063306952) and add it to both sides. Add '0.8063306952' to each side of the equation. -1.795918367x + 0.8063306952 + x2 = 0.4897959184 + 0.8063306952 Reorder the terms: 0.8063306952 + -1.795918367x + x2 = 0.4897959184 + 0.8063306952 Combine like terms: 0.4897959184 + 0.8063306952 = 1.2961266136 0.8063306952 + -1.795918367x + x2 = 1.2961266136 Factor a perfect square on the left side: (x + -0.8979591835)(x + -0.8979591835) = 1.2961266136 Calculate the square root of the right side: 1.138475566 Break this problem into two subproblems by setting (x + -0.8979591835) equal to 1.138475566 and -1.138475566.Subproblem 1
x + -0.8979591835 = 1.138475566 Simplifying x + -0.8979591835 = 1.138475566 Reorder the terms: -0.8979591835 + x = 1.138475566 Solving -0.8979591835 + x = 1.138475566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8979591835' to each side of the equation. -0.8979591835 + 0.8979591835 + x = 1.138475566 + 0.8979591835 Combine like terms: -0.8979591835 + 0.8979591835 = 0.0000000000 0.0000000000 + x = 1.138475566 + 0.8979591835 x = 1.138475566 + 0.8979591835 Combine like terms: 1.138475566 + 0.8979591835 = 2.0364347495 x = 2.0364347495 Simplifying x = 2.0364347495Subproblem 2
x + -0.8979591835 = -1.138475566 Simplifying x + -0.8979591835 = -1.138475566 Reorder the terms: -0.8979591835 + x = -1.138475566 Solving -0.8979591835 + x = -1.138475566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8979591835' to each side of the equation. -0.8979591835 + 0.8979591835 + x = -1.138475566 + 0.8979591835 Combine like terms: -0.8979591835 + 0.8979591835 = 0.0000000000 0.0000000000 + x = -1.138475566 + 0.8979591835 x = -1.138475566 + 0.8979591835 Combine like terms: -1.138475566 + 0.8979591835 = -0.2405163825 x = -0.2405163825 Simplifying x = -0.2405163825Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0364347495, -0.2405163825}
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